The following is a brief review of three landmark papers of Peter Bickel on theoretical and methodological aspects of nonparametric density and regression estimation and the related topic of goodness-of-fit testing, including a class of semiparametric goodness-of-fit tests. We consider the context of these papers, their contribution and their impact. Bickel’s first work on density estimation wa...

Intermittent fault localization approaches account for the fact that faulty components may fail intermittently by considering a parameter (known as goodness) that quantifies the probability that faulty components may still exhibit correct behavior. Current, state-of-the-art approaches (1) assume that this goodness probability is context independent and (2) do not provide means for integrating p...

It has been said that “goodness without knowledge is weak and feeble, yet knowledge without goodness is dangerous.”1 Peter Diamond is one of those extremely rare people who combine knowledge and goodness. Indeed—and I hope this doesn’t offend anyone in the room—Peter is probably the smartest person I know. In addition to that, he is simply a wonderful person and colleague. I am thrilled that th...

In this paper we review the goodness-of-fit problem for assessing whether a sample is consistentwith the Pareto-type model. To this end we introduce a general kernel goodness-of-fit statistic. Thederivation of the proposed class is based on the close link between the strict Pareto and the exponentialdistribution and puts some of the available goodness-of-fit procedures for the latte...

Polygonal hybrid systems (SPDIs) are planar hybrid systems, whose dynamics are defined in terms of constant differential inclusions, one for each of a number of polygonal regions partitioning the plane. The reachability problem for SPDIs is known to be decidable, but depends on the goodness assumption — which states that the dynamics do not allow a trajectory to both enter and leave a region th...

In this paper, we employ fixed point theory and semidefinite programming to compute the performance bounds on convex block-sparsity recovery algorithms. As a prerequisite for optimal sensing matrix design, a computable performance bound would open doors for wide applications in sensor arrays, radar, DNA microarrays, and many other areas where block-sparsity arises naturally. We define a family ...

Other things being equal, people prefer simpler explanations to more complex ones. However, complex explanations often provide better fits to the observed data, and goodness-of-fit must therefore be traded off against simplicity to arrive at the most likely explanation. In three experiments, we examine how people negotiate this tradeoff. As a case study, we investigate laypeople’s intuitions ab...

Several goodness-of-fit tests of a lifetime distribution have been suggested in the literature; many take into account censoring and/or truncation of event times. In some contexts, a goodness-of-fit test for the truncation distribution is of interest. In particular, better estimates of the lifetime distribution can be obtained when knowledge of the truncation law is exploited. In cross-sectiona...

Auditory speech is difficult to discern in degraded listening conditions, however the addition of visual speech can improve perception. The Perceptual Assimilation Model [1] suggests that non-native contrasts involving a native phonological difference (two-category assimilation) should be discriminated more accurately than those involving a phonetic goodness-offit difference (category-goodness ...